A multi-component mathematical model for thrombin production in flowing blood has been developed for the first time and used to explore the possible effects of the entire blood coagulation reaction network structure as well as blood flow and bulk protein concentrations on thrombin production.

The common pathway was first examined assuming constant factor IXa concentration, under two limiting situations:​ The Sparsely Covered Membrane (SCM) Model, which assumes an excess of membrane sites, and the Densely Covered Membrane (DCM) Model, where membrane site competition and saturation were taken into consideration.

In the SCM Model an analysis of reaction network structure showed that feedback activation of factor V and factor VIII by thrombin leads to the appearance of multiple steady states, long induction periods in thrombin versus time simulations and robustness with respect to changes in zymogen concentrations, above ≈10% or normal physiological concentrations. In the region of intermediate mass transfer rates, where two stable steady states exist, initial thrombin concentrations greater than the order of 10nM were required in order for thrombin production to reach the upper steady state. The lower steady state occurred at extremely low thrombin concentrations, not sufficient for thrombus formation. At low mass transfer rates, corresponding to stagnant regions, extremely long induction periods followed by a large burst of thrombin production were observed.

In the DCM Model it was found that tightly bound prothrombinase and tenase complexes dominate the membrane sites. Competition between these two complexes resulted in factor IX and factor VIII having an inhibiting effect on thrombin production, no matter which of the two complexes bound more tightly. The "bound" and "free" substrate models were compared, where it was found that the bound substrate model led to multiplicities, however only at protein concentrations well out of the physiological range.

A model of the extrinsic pathway up to the production of factor Xa was developed and the results were shown to compare favourably with experimental results contained in Repke et al¹. The whole intrinsic pathway was studied by linking the contact activation reactions with the common pathway. Here it was found that the maximum, not steady state, factor IXa concentration determined the subsequent events. In addition, a study of the sensitivity of the thrombin production to the extent of the common pathway reactions yielded unexpected results.

Finally, recommendations have been made for experimental work to verify the above results.